1963
DOI: 10.1017/s0022112063001439
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Some perturbation solutions in laminar boundary-layer theory

Abstract: The velocity fields associated with a variety of flows which may be described by perturbations of the Blasius solution are considered. These are flows which, for example, because of localized mass transfer, involve the initial-value problem of boundary-layer theory, or which involve a variable ratio of the viscosity-density product, or finally which involve mass transfer. The perturbation solutions are presented so that in accord with the usual linearization procedures further applications for the determinatio… Show more

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Cited by 98 publications
(72 citation statements)
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“…The streamwise, cross-flow velocity profiles and the //-profile (normalized with their máxima in 0 < f < oo) are plotted in figure 2, and the máxima of U, V, W and H are plotted versus x with solid lines in figure 3(a). As already noticed by Luchini (2000), figure 2{a) shows that the streamwise velocity of the optimal perturbation remains approximately constant, up to rescaling, and approximately equal to both the streamwise velocity of the first Libby-Fox mode, U = í;F" (Stewartson 1957;Libby & Fox 1964;and Luchini 1996) and the streamwise velocity of the first Luchini mode; these two are also plotted for comparison. Figure 2 also shows that the new variable H introduced above also remains approximately constant and approximately equal to U (when rescaled with its máximum), which suggests that a low-dimensional Ordinary Differential Equation (ODE) model of streaks should be possible.…”
Section: Resultsmentioning
confidence: 62%
“…The streamwise, cross-flow velocity profiles and the //-profile (normalized with their máxima in 0 < f < oo) are plotted in figure 2, and the máxima of U, V, W and H are plotted versus x with solid lines in figure 3(a). As already noticed by Luchini (2000), figure 2{a) shows that the streamwise velocity of the optimal perturbation remains approximately constant, up to rescaling, and approximately equal to both the streamwise velocity of the first Libby-Fox mode, U = í;F" (Stewartson 1957;Libby & Fox 1964;and Luchini 1996) and the streamwise velocity of the first Luchini mode; these two are also plotted for comparison. Figure 2 also shows that the new variable H introduced above also remains approximately constant and approximately equal to U (when rescaled with its máximum), which suggests that a low-dimensional Ordinary Differential Equation (ODE) model of streaks should be possible.…”
Section: Resultsmentioning
confidence: 62%
“…The value of B 1 cannot be determined by the large-ξ analysis sinceξ −2 G 1 (η) is an eigensolution of the perturbation equation. The next term in the expansion is O(ξ −α ), α ≈ 3.774, the fractional power arising as the next eigensolution of an infinite sequence (Libby & Fox, 1963). It appears that B 1 , together with the set of similar constants appearing in higher-order terms, is dependent on conditions close to the nose of the body and hence can be determined only by numerical integration from ξ = 0.…”
Section: Steady Boundary Layer Equationmentioning
confidence: 99%
“…For all γ > 0, G γ has solutions which decay algebraically as η → ∞, but only for certain γ do solutions exist which decay exponentially at infinity. Libby & Fox (1963) give the first 10 eigenvalues. The first such eigenvalue, γ 1 = 2 has already been discussed.…”
Section: Steady Flowmentioning
confidence: 99%